Answer
$dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$
Work Step by Step
Given: $m=p^{5}q^{3}$
The differential form can be evaluated as follows:
$dw=\dfrac{\partial w}{\partial x} dx + \dfrac{\partial w}{\partial y} dy $
We need to find the partial derivatives w.r.t. $p$ and $q$ as follows:
$dm= \dfrac{\partial m}{\partial p}dp+\dfrac{\partial m}{\partial q}dq$
Here, we get $ \dfrac{\partial m}{\partial p}dp=(5) p^{4}q^{3}dp$
and $\dfrac{\partial m}{\partial q}dq=(3) p^{5}q^{2}dq$
Hence, we have $dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$
